SIAM INTERNATIONAL MATH AND
SCIENCE OLYMPICS NATIONAL ROUND 2024
VÒNG QUỐC GIA KỲ THI OLYMPIC
TOÁN VÀ KHOA HỌC QUỐC TẾ SIMSO 2024
Question Paper for Mathematics
Phiếu câu hỏi Môn Toán
SENIOR SECONDARY – KHỐI 11 + 12
Time allowed: 90 minutes
Thời gian thi: 90 phút
Instructions to Contestants: (Hướng dẫn thi)
1.
Each contestant should have ONE Question-Answer Book which CANNOT be taken
away.
Mỗi thí sinh được cấp MỘT bộ Phiếu câu hỏi - Phiếu trả lời. Thí sinh KHÔNG ĐƯỢC mang tài
liệu ra ngoài phòng thi.
2.
This test has 30 Multiple Choice questions (5 marks each). The highest possible score is
150. No points shall be deducted for blank or incorrect answers.
Bài thi có 30 câu hỏi trắc nghiệm (mỗi câu 5 điểm). Tổng số điểm tối đa là 150. Mỗi câu trả lời sai
hoặc không trả lời thì không có điểm.
3.
All answers should be filled in the ANSWER SHEET.
Tất cả đáp án phải được tô vào PHIẾU TRẢ LỜI.
4.
NO calculators can be used during the contest.
Tuyệt đối KHÔNG sử dụng máy tính trong quá trình thi.
5. This Question-Answer Book will be collected at the end of the contest.
Bộ Phiếu câu hỏi – Phiếu trả lời sẽ được thu lại sau khi thí sinh hoàn thành bài thi.
6. DO NOT turn over this Question-Answer Book without approval of the examiner.
Thí sinh KHÔNG tự ý xem đề khi chưa có hiệu lệnh của giám thị.
Otherwise, contestant may be DISQUALIFIED.
Nếu thí sinh vi phạm một trong các điều trên, BTC có quyền hủy kết quả thi của thí sinh đó.
1
KỲ THI OLYMPIC TOÁN VÀ KHOA HỌC QUỐC TẾ SIMSO 2024
Siam International Math and Science Olympics 2024
SENIOR SECONDARY / KHỐI 11 + 12
1. Find all positive divisors of 441.
a. 1 , 441
b. 3 , 7 , 9 , 21 , 49 , 63 , 147
c. 1 , 3 , 7 , 9 , 21 , 441
d. 1 , 3 , 7 , 9 , 21 , 49 , 63 , 147 , 441
e. None of the above
2. What is the prime factorization of 9828?
a. 22 · 32 · 7 · 13
b. 22 · 33 · 13
c. 22 · 33 · 7 · 13
d. 22 · 33 · 7
e. 22 · 32 · 7 · 18
3. Convert 1234510 to base 2.
a. 110000001110012
b. 110100001110012
c. 111000001110012
d. 110010001110012
e. 1100001111110012
1
4. What is the last digit in the decimal expansion of 256?
a. 6
b. 5
c. 4
d. 2
e. 0
5. Every 12 hours, Clark Kent’s standard clock advances 19 hours. If Clark Kent’s clock is
correct at 6am on the morning of June 1st, what time will his clock read at 6am on the morning
of July 1st?
a. 6pm
b. 12am
c. 12pm
d. 6am
e. 9am
6. During the SIMSO National Round Examinations, Robert writes his full name
ROBERTFORDAN over and over again on a sheet of paper. He completed 1000 letters before
the paper was taken away by the proctor and asked him to finish the examination. What was
the last letter that he wrote?
a. R
b. E
c. F
d. D
e. T
7. The third and sixth terms of a convergent geometric series are 18 and −
the first term of the series.
a. 8
b. - 40.5
c. - 8
d. 40.5
16
respectively. Find
3
e. 2
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KỲ THI OLYMPIC TOÁN VÀ KHOA HỌC QUỐC TẾ SIMSO 2024
Siam International Math and Science Olympics 2024
SENIOR SECONDARY / KHỐI 11 + 12
8. The first three terms of a geometric series are: x + 1, x − 1, 2x − 5. Calculate the greatest value
of x (x ≠ 1 or -1).
a. 2
b. 3
c. 4
d. 5
e. 6
9. Surachai is saving money to buy a new video game that costs 1200 Thai Baht. He starts by
saving 20 Baht on the first day. Each day after, he saves 10 Baht more than he did the previous
day. How many days will it take for Surachai to save enough money for the video game?
a. 10
b. 15
c. 20
d. 25
e. 30
10. Three suspects, Pai, Kwan, and Somchai, are being interrogated about a stolen temple
treasure. They are known to be one Truth-teller (always tells the truth) and two Liars (always
lie). Here are their statements:
Pai: "Somchai stole the treasure."
Kwan: "Pai is a Liar."
Somchai: "Kwan and I are both Liars."
Which of the following is definitely true?
a. Kwan and Somchai are both Liars.
b. Kwan is the Truth-teller.
c. Kwan is a Liar.
d. Pai is the Truth-teller.
e. Somchai is the Truth-teller.
11. Find the eighth term of the sequence: 3, 9, 27, 81, 243, 729,…
a. 2187
b. 821
c. 6561
d. 19683
e. 19886
12. Families living in ICE City are biking. There are a total of 2022 families in the city each with
two or four bicycles. Given that there are as many families owning either four bicycles as many
families owning two bicycles, how many bicycles are there in ICE City?
a. 2022
b. 3033
c. 4044
d. 5055
e. 6066
13. What is the least common denominator for the expression
𝑛+3
𝑛2 −4
− 2
7
𝑛 +7𝑛+10
?
a. (𝑛 + 2)(𝑛 − 2)(𝑛 + 5)
b. (𝑛 + 2)(𝑛 − 2)
c. (𝑛 + 2)(𝑛 + 5)
d. (𝑛 + 2)(𝑛 − 2)(𝑛 + 2)(𝑛 + 5)
e. (𝑛 + 2)(𝑛 − 2)(𝑛 + 4)(𝑛 + 2)
3
KỲ THI OLYMPIC TOÁN VÀ KHOA HỌC QUỐC TẾ SIMSO 2024
Siam International Math and Science Olympics 2024
SENIOR SECONDARY / KHỐI 11 + 12
14. Solve the equation 17 − 8𝑥 = −9𝑥 − 8.
1
b. 𝑥 = 25
c. 𝑥 = 9
a. 𝑥 = 25
d. 𝑥 = 3
e. 𝑥 = −25
15. How many integral solutions are there for x if 1234 ≤ 𝑥 2 + 100 ≤ 2024?
a. 4
b. 5
c. 8
d. 10
16. Let 𝑟1 and 𝑟2 be the roots of the equation 𝑥 2 − 2024𝑥 + 2024 = 0 . Find
a.
1010
1011
b.
1011
1012
c.
1012
1013
d.
1013
1014
1
𝑟12
e. 20
1
+ 2.
𝑟2
e.
1014
1015
17. What is the sum of the roots of 𝑎𝑥 2 − 2022𝑥 − 2023 = 0 if a = 3?
a. 674
b. 1010
c. 864
d. 900
e. 1024
18. Find the product of the nth roots of 1.
a. 0
b. 1
c. 2
e. 4
d. 3
1
the radius of circle B. Circle A rolls around circle B one trip back
3
to its starting point. How many times will circle A rotate in total?
a. 2
b. 3
c. 4
d. 5
e. 6
19. The radius of circle A is
20. A copper wire when bent in the form of a square encloses an area of 544 sq cm. The same
wire is now bent in the form of a circle. What is the area enclosed by the circle in cm2? (Choose
the nearest answer)
a. 490 cm2
b. 510 cm2
c. 590 cm2
d. 610 cm2
e. 690 cm2
21. Find the height of a pentagonal prism with volume 6 and base area 9. Start with an equation
that relates the base area B, height h, and volume V:
1
1
2
3
a.
b.
c.
d.
2
3
3
5
e. None of the above
22. GEOM is a square that encloses 2 circular arcs A and B such that A is centered at E and
intersects G and O while B is centered at M and intersects G and O. Diagonal EM passes
through the arcs at points C and D. Given that CD = 30 − 15√2, what is the perimeter of the
square?
a. 40
b. 48
c. 54
d. 56
e. 60
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KỲ THI OLYMPIC TOÁN VÀ KHOA HỌC QUỐC TẾ SIMSO 2024
Siam International Math and Science Olympics 2024
SENIOR SECONDARY / KHỐI 11 + 12
23. Given the figure below, the radii of 2 identical bigger circles are 6 cm each and the distance
between their centers is 16 cm. If the radius of the smallest circle at the top is 3 cm, what is the
shortest distance from the center of the topmost circle to line m?
a. 6 + √17 cm
b. 3 + √12 cm
c. 6 + √21 cm
d. √17 cm
24. What is the area of a quadrant of a circle whose circumference is 28.5 cm?
a. 13.50 cm2
b. 15.67 cm2
c. 16.16 cm2
d. 16.90 cm2
e. 2√17 cm
e. 17.50 cm2
25. How many whole numbers less than 100 are multiples of 3 but not multiples of 5?
a. 15
b. 23
c. 27
d. 29
e. 33
26. If 99 people stand in a circle, and each shakes the hand of the person on each side, how
many handshakes are there all together?
a. 98
b. 99
c. 198
d. 200
e. None of the above
27. How many distinct scalene triangles can be formed by connecting three vertices of a regular
nonagon?
a. 54
b. 84
c. 57
d. 24
e. 33
28. How many different license plates are possible if each one is 3 letters followed by 3 digits
if the letters and digits cannot be repeated?
a. 78624
b. 1757600
c. 5616000
d. 860000
e. 11232000
29. Find the coefficient of the term x5y3 in the expansion of (3x − 2y)8 .
a. 207746
b. -158648
c. -246881
d. -108864
e. 100254
30. A lock will open with the correct choice of 3 numbers from 0 to 99 inclusive in correct order.
How many different sets of 3 numbers are there if the numbers cannot repeat?
a. 8100
b. 10000
c. 161700
d. 970200
e. 1000000
5
KỲ THI OLYMPIC TOÁN VÀ KHOA HỌC QUỐC TẾ SIMSO 2024
Siam International Math and Science Olympics 2024
SENIOR SECONDARY / KHỐI 11 + 12